Robust control of self-adjoint distributed-parameter structures

This paper examines the active vibration control-of distributed-parameter structures in which a self-adjoint differential operator expresses the stiffness distribution. For large and complex structures, computational requirements and/or modeling limitations ensure that a reduced-order controller is used. However, although in practice only discrete actuators and discrete sensors are available, spatially distributed control forces and spatially distributed observations are desirable for implementing a reduced-order controller. Therefore a distinction arises among 1) designing distributed control forces for a reduced-order model, 2) implementing the control forces with a number of actuators, and 3) estimating the distributed state from a number of sensors. Herein the distinctions are realized by introducing three appropriate projection operations. The effects of the three projections on the actual closed-loop eigenvalues are investigated in detail. A criterion for the controller to be robust in the stability sense is discussed and illustrative examples are presented.